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By B. Banaschewski (auth.), Horst Herrlich, Gerhard Preuß (eds.)

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Extra info for Categorical Topology: Proceedings of the International Conference, Berlin, August 27th to September 2nd, 1978

Example text

X ~ B = U{Bnl and statements is a c o u n t a b l e is D - c l o s e d call Y 6 E) spaces. 1 implies to c l o s e d X: B £ ~ Furthermore space [6] products. respect for f u n c t i o n a l the c l a s s following semistratifiable that X 6 E reader to the b i r e f l e c t i v e developable (3) of f i n i t e property. 4 T H E O R E M (I) and is left to the fullfills of t o p o l o g i c a l t h a t E is c l o s e d w i t h >Y c l o s e d Then The p r o o f the f o r m a t i o n intersection in a d d i t i o n mappings spaces under class ~ closed and e v e r y this coarser property 33 R - t o p o l o g y on X w h i c h is T - s e p a r a t e d w i t h r e s p e c t to o o a l l D - c l o s e d s u b s e t s of X is T - s e p a r a t e d w i t h r e s p e c t to -- o X.

E. respect - to the b e s t the mapping X: X = 0 and that {D 2} h a s for discrete an E - c l o s e d result. with an a r b i t r a r y to coarser D 2 is t h e case X belongs every Y is c l o s e d . mapping. is e q u i v a l e n t following ind X = O and To-saturated that , where In t h i s is a d e q u a t e a space an u l t r a n o r m a l rated E = {D2} points. and that X £ N({D2}) the class two such Ti-space clopen-to-closed is w e l l - k n o w n and an a r b i t r a r y exactly intersection It into space spaces [I].

6 w a s general announced theorem in [3] w i t h o u t is c o n t a i n e d in proof. A [4]. Bing , Metrization (1951) 1 7 5 - 1 8 6 . Brandenburg , HOllenbildungen wickelbaren topologischen R~ume B e r l i n (1978). Brandenburg , O n a c l a s s o f n e a r n e s s s p a c e s a n d the e p i r e f l e c t i v e h u l l of d e v e l o p a b l e t o p o l o g i c a l s p a c e s , to a p p e a r in the P r o c . of Int. S y m p . on T o p . a n d its A p p l . , B e o g r a d (1977). Broughan , I n v a r i a n t s for R e a l - G e n e r a t e d Uniform Topological and Algebraic Categories , L e c t .

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